Observations on the parity of the total number of parts in odd--part partitions.
Sellers, James A. (2007)
Integers
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Displaying similar documents to “Arithmetic properties for hyper -ary partition functions.”
Observations on the parity of the total number of parts in odd--part partitions.
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Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first...
Extending a recent result of Santos on partitions into odd parts.
Sellers, James A. (2003)
Integers
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